Advanced Lane Finding Project¶
The goals / steps of this project are the following:
- Compute the camera calibration matrix and distortion coefficients given a set of chessboard images.
- Apply a distortion correction to raw images.
- Use color transforms, gradients, etc., to create a thresholded binary image.
- Apply a perspective transform to rectify binary image ("birds-eye view").
- Detect lane pixels and fit to find the lane boundary.
- Determine the curvature of the lane and vehicle position with respect to center.
- Warp the detected lane boundaries back onto the original image.
- Output visual display of the lane boundaries and numerical estimation of lane curvature and vehicle position.
In [1]:
import numpy as np
import cv2
import glob
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
In [2]:
plt.rcParams["figure.figsize"] = (9,12)
In [3]:
fnames = glob.glob('camera_cal/calibration*.jpg')
n_col = 4
n_row = int(np.ceil(len(fnames)/n_col))
f, axs = plt.subplots(n_row, n_col, figsize=(20,3*n_row))
axs = axs.ravel()
for i in range(len(axs)):
if i < len(fnames):
axs[i].axis('off')
image = mpimg.imread(fnames[i])
axs[i].imshow(image)
else:
f.delaxes(axs[i])
Camera Calibration¶
Two main steps:
- Use chessboard images to obtain image points and object points
- Use OpenCV functions
cv2.calibrateCamera()andcv2.undistort()to compute the calibration and undistortion.
Image points and object points¶
I used OpenCV to convert the image to grayscale first, then used the functions findChessboardCorners() and drawChessboardCorners() to automatically find and draw corners in the chessboard images.
I observed that there are 9 inside corners in the row, 6 inside corners in the column, and stored them in nx and ny.
I start by preparing object points, which will be the (x, y, z) coordinates of the chessboard corners in the world. Here I am assuming the chessboard is fixed on the (x, y) plane at z=0, such that the object points are the same for each calibration image. Thus, objp is just a replicated array of coordinates, and objpoints will be appended with a copy of it every time I successfully detect all chessboard corners in a test image. imgpoints will be appended with the (x, y) pixel position of each of the corners in the image plane with each successful chessboard detection.|
In [4]:
nx = 9
ny = 6
# Make a list of calibration images
img_index = 4
test_img = mpimg.imread(fnames[img_index])
# Convert to grayscale
gray = cv2.cvtColor(test_img, cv2.COLOR_RGB2GRAY)
# Find the chessboard corners
ret, corners = cv2.findChessboardCorners(gray, (nx, ny), None)
# If found, draw corners
if ret == True:
# Draw and display the corners
cv2.drawChessboardCorners(test_img, (nx, ny), corners, ret)
plt.axis('off')
plt.imshow(test_img)
In [5]:
def generate_points(fnames):
# prepare object points, like (0,0,0), (1,0,0), (2,0,0) ....,(6,5,0)
objp = np.zeros((ny*nx,3), np.float32)
objp[:,:2] = np.mgrid[0:nx,0:ny].T.reshape(-1,2)
# Arrays to store object points and image points from all the images.
objpoints = [] # 3d points in real world space
imgpoints = [] # 2d points in image plane.
for fname in sorted(fnames):
img = mpimg.imread(fname)
gray = cv2.cvtColor(img,cv2.COLOR_RGB2GRAY)
img_width, img_height = gray.shape[1], gray.shape[0]
# Find the chessboard corners
ret, corners = cv2.findChessboardCorners(gray, (nx,ny), None)
# If found, add object points, image points
if ret == True:
objpoints.append(objp)
imgpoints.append(corners)
return objpoints, imgpoints
objpoints, imgpoints = generate_points(fnames)
Camera calibration matrix and distortion coefficient¶
I then used the output objpoints and imgpoints to compute the camera calibration and distortion coefficients using the cv2.calibrateCamera() function. I applied this distortion correction to the test image using the cv2.undistort() function and obtained this result:
In [6]:
ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, gray.shape[::-1], None, None)
In [7]:
def show_images(img1, img2, title1='Original Image', title2='New Image', fsize=30):
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(24, 9))
f.tight_layout()
ax1.imshow(img1)
ax1.set_title(title1, fontsize=fsize)
ax2.imshow(img2, cmap='gray')
ax2.set_title(title2, fontsize=fsize)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)
In [8]:
test_img = mpimg.imread(fnames[0])
undist = cv2.undistort(test_img, mtx, dist, None, mtx);
show_images(test_img, undist, title2='Undistorted Image')
Pipeline (single images)¶
Undistort image¶
In [9]:
def undistort(img):
undist = cv2.undistort(img, mtx, dist, None, mtx)
return undist
test_img = mpimg.imread('test_images/test3.jpg')
undist = undistort(test_img)
show_images(test_img, undist, title2='Undistorted Image')
Color Threshold¶
Explore test images in different color spaces, observe which makes the lane lines stand out.
In [10]:
def convert_color_space(img, color_space='RGB'):
if color_space != 'RGB':
if color_space == 'HSV':
new_image = cv2.cvtColor(img, cv2.COLOR_RGB2HSV)
elif color_space == 'LUV':
new_image = cv2.cvtColor(img, cv2.COLOR_RGB2LUV)
elif color_space == 'LAB':
new_image = cv2.cvtColor(img, cv2.COLOR_RGB2LAB)
elif color_space == 'HLS':
new_image = cv2.cvtColor(img, cv2.COLOR_RGB2HLS)
elif color_space == 'YUV':
new_image = cv2.cvtColor(img, cv2.COLOR_RGB2YUV)
elif color_space == 'YCrCb':
new_image = cv2.cvtColor(img, cv2.COLOR_RGB2YCrCb)
else: new_image = np.copy(img)
return new_image
def show_color_spaces(img, color_spaces=['RGB', 'HSV', 'YUV', 'HLS', 'LUV', 'LAB'], cmap=None):
for color in color_spaces:
new_image = convert_color_space(img, color)
f, axs = plt.subplots(1, 4, figsize=(16,3))
axs = axs.ravel()
for i in range(len(axs)):
axs[i].axis('off')
if i == 0:
axs[i].imshow(new_image)
else:
axs[i].imshow(new_image[:,:,i-1], cmap='gray')
title = color if i == 0 else color[i-1] + ' Channel'
axs[i].set_title(title)
In [11]:
test_image = mpimg.imread('test_images/test1.jpg')
show_color_spaces(test_image)
In [12]:
def color_binary(img):
hsv = convert_color_space(img, 'HSV')
YELLOW_MIN1 = np.array([0, 90, 200],np.uint8)
YELLOW_MAX1 = np.array([50, 255, 255],np.uint8)
yellow1 = cv2.inRange(hsv, YELLOW_MIN1, YELLOW_MAX1)
lab = convert_color_space(img, 'LAB')
yellow2 = np.zeros_like(lab[:,:,2])
yellow2[(lab[:,:,2] > 150)] = 1
WHITE_MIN = np.array([0, 0, 220],np.uint8)
WHITE_MAX = np.array([179, 70, 255],np.uint8)
white = cv2.inRange(hsv, WHITE_MIN, WHITE_MAX)
white2 = np.zeros_like(hsv[:,:,2])
white2[(hsv[:,:,2] > 210)] = 1
# Remove trees on roadside
green = cv2.inRange(hsv, (30, 60, 100), (120, 255, 255))
binary = np.zeros_like(hsv[:,:,0])
binary[((yellow1 == 255) | (yellow2 == 1) | (white == 255) | (white2 == 1)) & (green==0)] = 1
return binary
In [13]:
image = mpimg.imread('test_images/test3.jpg')
s_binary = color_binary(image)
show_images(image, s_binary, title2='HSV Binary')
Gradient Threshold¶
Explore the effects of sobel gradient in x direction, y direction, magnitude, or specific direction.
In [14]:
def abs_sobel_thresh(channel, orient='x', sobel_kernel=3, thresh=(0, 255)):
if orient == 'x':
sobel = cv2.Sobel(channel, cv2.CV_64F, 1, 0)
else:
sobel = cv2.Sobel(channel, cv2.CV_64F, 0, 1)
abs_sobel = np.absolute(sobel)
scaled_sobel = np.uint8(255*abs_sobel/np.max(abs_sobel))
binary_output = np.zeros_like(scaled_sobel)
binary_output[(scaled_sobel>thresh[0]) & (scaled_sobel<thresh[1])] = 1
return binary_output
In [15]:
test_image = mpimg.imread('test_images/test1.jpg')
v_channel = convert_color_space(test_image, 'LUV')[:, :, 2]
v_binary = abs_sobel_thresh(v_channel, orient='x', thresh=(20, 50))
show_images(test_image, v_binary, title2='Thresholded Gradient - X')
In [16]:
test_image = mpimg.imread('test_images/test1.jpg')
v_channel = convert_color_space(test_image, 'LUV')[:, :, 2]
v_binary = abs_sobel_thresh(v_channel, orient='y', thresh=(20, 50))
show_images(test_image, v_binary, title2='Thresholded Gradient - Y')
Y-gradient does a cleaner job for picking up the lane lines.
In [17]:
def mag_thresh(channel, x_ksize=3, y_ksize=3, mag_thresh=(0, 255)):
sobelx = cv2.Sobel(channel, cv2.CV_64F, 1, 0, ksize=x_ksize)
sobely = cv2.Sobel(channel, cv2.CV_64F, 0, 1, ksize=y_ksize)
magnitude = (sobelx**2 + sobely**2)**.5
scale_magnitude = np.uint8(255*magnitude/np.max(magnitude))
binary_output = np.zeros_like(channel)
binary_output[(scale_magnitude > mag_thresh[0]) & (scale_magnitude < mag_thresh[1])] = 1
return binary_output
In [18]:
test_image = mpimg.imread('test_images/test3.jpg')
v_channel = convert_color_space(test_image, 'LUV')[:,:,2]
mag_binary = mag_thresh(v_channel, x_ksize=3, y_ksize=3, mag_thresh=(50,200))
show_images(test_image, mag_binary, title2='Mag Binary - V channel')
In [19]:
s_channel = convert_color_space(test_image, 'HLS')[:,:,2]
mag_binary = mag_thresh(s_channel, x_ksize=3, y_ksize=3, mag_thresh=(50,200))
show_images(test_image, mag_binary, title2='Mag Binary - L channel')
In [20]:
def dir_threshold(channel, sobel_kernel=3, thresh=(0, np.pi/2)):
sobelx = cv2.Sobel(channel, cv2.CV_64F, 1, 0, ksize=sobel_kernel)
sobely = cv2.Sobel(channel, cv2.CV_64F, 0, 1, ksize=sobel_kernel)
abs_sobelx = np.absolute(sobelx)
abs_sobely = np.absolute(sobely)
grad_direct = np.arctan2(abs_sobely, abs_sobelx)
binary_output = np.zeros_like(channel)
binary_output[(grad_direct > thresh[0]) & (grad_direct < thresh[1])] = 1
return binary_output
In [21]:
test_image = mpimg.imread('test_images/test2.jpg')
v_channel = convert_color_space(test_image, 'HSV')[:,:,2]
dir_binary = dir_threshold(v_channel, sobel_kernel=3, thresh=(0.9, 1.1))
show_images(test_image, dir_binary, title2='(HS)V Directional Binary')
In [22]:
def gradient_binary(img):
luv = convert_color_space(img, 'LUV')
luv = cv2.medianBlur(luv, 3)
v_channel = luv[:,:,2]
v_binary = mag_thresh(v_channel, x_ksize=3, y_ksize=3, mag_thresh=(50,200))
s_channel = convert_color_space(img, 'HLS')[:,:,2]
s_binary = mag_thresh(s_channel, x_ksize=3, y_ksize=3, mag_thresh=(50,200))
binary = np.zeros_like(v_channel)
binary[(s_binary == 1) | (v_binary == 1)] = 1
return binary
In [23]:
test_image = mpimg.imread('test_images/test1.jpg')
grad_binary = gradient_binary(test_image)
show_images(test_image, grad_binary, title2='Gradient Binary')
In [24]:
def thresholded_binary(img):
cbinary = color_binary(img)
grad_binary = gradient_binary(img)
combined_binary = np.zeros_like(cbinary)
combined_binary[(cbinary == 1) | (grad_binary == 1)] = 1
return combined_binary
In [25]:
#test_image = mpimg.imread('test_images/test2.jpg')
thresh_binary = thresholded_binary(undist)
show_images(test_img, thresh_binary, title2='Combined color and gradient thresholds')
Perspective Transform¶
In [26]:
img_size = (test_image.shape[1], test_image.shape[0])
min_y = img_size[1] *2 / 3
max_y = img_size[1] * 0.9
src = np.float32(
[[(img_size[0] / 2) - 89, min_y],
[(img_size[0] * 297/1280), max_y],
[(img_size[0] * 1001/1280), max_y],
[(img_size[0] / 2 + 90), min_y]])
dst = np.float32(
[[(img_size[0] / 4), 0],
[(img_size[0] / 4), max_y],
[(img_size[0] * 3 / 4), max_y],
[(img_size[0] * 3 / 4), 0]])
# print(src)
# print(dst)
def warper(undist, img_size, src=src, dst=dst):
M = cv2.getPerspectiveTransform(src, dst)
Minv = cv2.getPerspectiveTransform(dst, src)
warped = cv2.warpPerspective(undist, M, (img_size[1], img_size[0]))
return warped, M, Minv
In [27]:
straight_image = mpimg.imread('test_images/straight_lines1.jpg')
# undist = cv2.undistort(test_image, mtx, dist, None, mtx);
straight_image_copy = straight_image.copy()
cv2.polylines(straight_image_copy,np.array([src], np.int32),True,(255,0,0), thickness=3)
straight_top_down, perspective_M, Minv = warper(straight_image, undist.shape)
straight_top_down_copy = straight_top_down.copy()
cv2.polylines(straight_top_down, np.array([dst], np.int32),True,(255,0,0), thickness=3)
show_images(straight_image_copy, straight_top_down, title1='Undistorted image with source points drawn', title2='Warped result with dest. points drawn', fsize=30)
In [28]:
top_down, perspective_M, Minv = warper(thresh_binary, img_size=thresh_binary.shape)
show_images(thresh_binary, top_down, title1='Undistorted image with source points drawn', title2='Warped result with dest. points drawn', fsize=30)
Detect Lane Pixels¶
I now have a thresholded warped image. Next, I need to decide explicitly which pixels are part of the lines, and which belong to the left line and which belong to the right line.
I first take a histogram along all the columns in the lower half of the image like following:
In [29]:
def x_bases(top_down_binary, plot=False):
histogram = np.sum(top_down_binary[top_down_binary.shape[0]//2:int(top_down_binary.shape[0]*0.9),:], axis=0)
midpoint = np.int(histogram.shape[0]/2)
leftx_base = np.argmax(histogram[:midpoint])
rightx_base = np.argmax(histogram[midpoint:]) + midpoint
if plot:
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(24, 7))
f.tight_layout()
ax1.plot(histogram)
ax1.set_title('Line Finding: Peaks in Histogram', fontsize=30)
ax2.imshow(top_down_binary, cmap='gray')
ax2.set_title('Warped result', fontsize=30)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)
return leftx_base, rightx_base
leftx_base, rightx_base = x_bases(top_down, plot=True)
print('left X base: {}, right X base: {}'.format(leftx_base, rightx_base))
In [30]:
def nonzero(binary):
nonzero = binary.nonzero()
nonzeroy = np.array(nonzero[0])
nonzerox = np.array(nonzero[1])
return nonzeroy, nonzerox
def sliding_window(binary_warped, plot=False):
# Choose the number of sliding windows
nwindows = 12
# Set height of windows
window_height = np.int(binary_warped.shape[0]/nwindows)
nonzeroy, nonzerox = nonzero(binary_warped)
# Current positions to be updated for each window
leftx_current = leftx_base
rightx_current = rightx_base
out_img = np.dstack((binary_warped, binary_warped, binary_warped))*255
# Set the width of the windows +/- margin
margin = 70
# Set minimum number of pixels found to recenter window
minpix = 50
# Create empty lists to receive left and right lane pixel indices
left_lane_inds = []
right_lane_inds = []
# Step through the windows one by one
for window in range(nwindows):
# Identify window boundaries in x and y (and right and left)
win_y_low = binary_warped.shape[0] - (window+1)*window_height
win_y_high = binary_warped.shape[0] - window*window_height
win_xleft_low = leftx_current - margin
win_xleft_high = leftx_current + margin
win_xright_low = rightx_current - margin
win_xright_high = rightx_current + margin
# Draw the windows on the visualization image
if plot:
cv2.rectangle(out_img,(win_xleft_low,win_y_low),(win_xleft_high,win_y_high),
(0,255,0), 2)
if win_xright_high < binary_warped.shape[1] and win_xright_low > 0:
cv2.rectangle(out_img,(win_xright_low,win_y_low),(win_xright_high,win_y_high),
(0,255,0), 2)
# Identify the nonzero pixels in x and y within the window
good_left_inds = ((nonzeroy >= win_y_low) & (nonzeroy < win_y_high) &
(nonzerox >= win_xleft_low) & (nonzerox < win_xleft_high)).nonzero()[0]
if win_xright_high < binary_warped.shape[1] and win_xright_low > 0:
good_right_inds = ((nonzeroy >= win_y_low) & (nonzeroy < win_y_high) &
(nonzerox >= win_xright_low) & (nonzerox < win_xright_high)).nonzero()[0]
# Append these indices to the lists
left_lane_inds.append(good_left_inds)
if win_xright_high < binary_warped.shape[1] and win_xright_low > 0:
right_lane_inds.append(good_right_inds)
# If you found > minpix pixels, recenter next window on their mean position
if len(good_left_inds) > minpix:
leftx_current = np.int(np.mean(nonzerox[good_left_inds]))
if len(good_right_inds) > minpix:
rightx_current = np.int(np.mean(nonzerox[good_right_inds]))
# Concatenate the arrays of indices
left_lane_inds = np.concatenate(left_lane_inds)
right_lane_inds = np.concatenate(right_lane_inds)
# Extract left and right line pixel positions
leftx = nonzerox[left_lane_inds]
lefty = nonzeroy[left_lane_inds]
rightx = nonzerox[right_lane_inds]
righty = nonzeroy[right_lane_inds]
return leftx, lefty, rightx, righty, out_img
def fit_lines(leftx, lefty, rightx, righty, out_img=None):
# if len(leftx) == 0 or len(lefty) == 0 or len(rightx) == 0 or len(righty) == 0:
# return None, None
# Fit a second order polynomial to each
left_fit = np.polyfit(lefty, leftx, 2) if (len(lefty)>0 and len(leftx)>0) else None
right_fit = np.polyfit(righty, rightx, 2) if (len(righty)>0 and len(rightx)>0) else None
if out_img is not None:
#left_fit, right_fit = sliding_window(binary_warped)
ploty = np.linspace(0, out_img.shape[0]-1, out_img.shape[0] )
left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]
out_img[lefty, leftx] = [255, 0, 0]
out_img[righty, rightx] = [0, 0, 255]
plt.imshow(out_img)
plt.rcParams["figure.figsize"] = (10,5)
plt.plot(left_fitx, ploty, color='yellow')
plt.plot(right_fitx, ploty, color='yellow')
plt.xlim(0, 1280)
plt.ylim(720, 0)
return left_fit, right_fit
leftx, lefty, rightx, righty, out_img = sliding_window(top_down, plot=True)
left_fit, right_fit = fit_lines(leftx, lefty, rightx, righty, out_img=out_img)
In [31]:
def window_mask(width, height, img_ref, center,level):
output = np.zeros_like(img_ref)
output[int(img_ref.shape[0]-(level+1)*height):int(img_ref.shape[0]-level*height),max(0,int(center-width/2)):min(int(center+width/2),img_ref.shape[1])] = 1
return output
def find_window_centroids(image):
window_width = 50
window_height = 80 # Break image into 9 vertical layers since image height is 720
margin = 100 # How much to slide left and right for searching
window_centroids = [] # Store the (left,right) window centroid positions per level
window = np.ones(window_width) # Create our window template that we will use for convolutions
# First find the two starting positions for the left and right lane by using np.sum to get the vertical image slice
# and then np.convolve the vertical image slice with the window template
# Sum quarter bottom of image to get slice, could use a different ratio
l_sum = np.sum(image[int(3*image.shape[0]/4):,:int(image.shape[1]/2)], axis=0)
l_center = np.argmax(np.convolve(window,l_sum))-window_width/2
r_sum = np.sum(image[int(3*image.shape[0]/4):,int(image.shape[1]/2):], axis=0)
r_center = np.argmax(np.convolve(window,r_sum))-window_width/2+int(image.shape[1]/2)
# Add what we found for the first layer
window_centroids.append((l_center,r_center))
# Go through each layer looking for max pixel locations
for level in range(1,(int)(image.shape[0]/window_height)):
# convolve the window into the vertical slice of the image
image_layer = np.sum(image[int(image.shape[0]-(level+1)*window_height):int(image.shape[0]-level*window_height),:], axis=0)
conv_signal = np.convolve(window, image_layer)
# Find the best left centroid by using past left center as a reference
# Use window_width/2 as offset because convolution signal reference is at right side of window, not center of window
offset = window_width/2
l_min_index = int(max(l_center+offset-margin,0))
l_max_index = int(min(l_center+offset+margin,image.shape[1]))
l_center = np.argmax(conv_signal[l_min_index:l_max_index])+l_min_index-offset
# Find the best right centroid by using past right center as a reference
r_min_index = int(max(r_center+offset-margin,0))
r_max_index = int(min(r_center+offset+margin,image.shape[1]))
r_center = np.argmax(conv_signal[r_min_index:r_max_index])+r_min_index-offset
# Add what we found for that layer
window_centroids.append((l_center,r_center))
return window_centroids
def plot_window_centroids(window_centroids, warped):
window_width = 120
window_height = 80 # Break image into 9 vertical layers since image height is 720
margin = 100 # How much to slide left and right for searching
# If we found any window centers
if len(window_centroids) > 0:
# Points used to draw all the left and right windows
l_points = np.zeros_like(warped)
r_points = np.zeros_like(warped)
# Go through each level and draw the windows
for level in range(0,len(window_centroids)):
# Window_mask is a function to draw window areas
l_mask = window_mask(window_width,window_height,warped,window_centroids[level][0],level)
r_mask = window_mask(window_width,window_height,warped,window_centroids[level][1],level)
# Add graphic points from window mask here to total pixels found
l_points[(l_points == 255) | ((l_mask == 1) ) ] = 255
r_points[(r_points == 255) | ((r_mask == 1) ) ] = 255
# Draw the results
template = np.array(r_points+l_points,np.uint8) # add both left and right window pixels together
zero_channel = np.zeros_like(template) # create a zero color channel
template = np.array(cv2.merge((zero_channel,template,zero_channel)),np.uint8) # make window pixels green
warpage= np.dstack((warped, warped, warped))*255 # making the original road pixels 3 color channels
output = cv2.addWeighted(warpage, 1, template, 0.5, 0.0) # overlay the orignal road image with window results
# If no window centers found, just display orginal road image
else:
output = np.array(cv2.merge((warped,warped,warped)),np.uint8)
# Display the final results
plt.imshow(output)
plt.title('window fitting results')
plt.show()
window_centroids = find_window_centroids(top_down)
plot_window_centroids(window_centroids, top_down)
Now I know where the lines are. For the next frame of video I don't need to do the blind search again, instead, I can just search in the margin around the preivous line position like this:
In [32]:
def look_ahead_search(binary_warped, left_fit, right_fit, plot=False):
nonzeroy, nonzerox = nonzero(binary_warped)
margin = 100
left_lane_inds = ((nonzerox > (left_fit[0]*(nonzeroy**2) + left_fit[1]*nonzeroy +
left_fit[2] - margin)) & (nonzerox < (left_fit[0]*(nonzeroy**2) +
left_fit[1]*nonzeroy + left_fit[2] + margin)))
right_lane_inds = ((nonzerox > (right_fit[0]*(nonzeroy**2) + right_fit[1]*nonzeroy +
right_fit[2] - margin)) & (nonzerox < (right_fit[0]*(nonzeroy**2) +
right_fit[1]*nonzeroy + right_fit[2] + margin)))
if plot:
# Generate x and y values for plotting
ploty = np.linspace(0, binary_warped.shape[0]-1, binary_warped.shape[0] )
left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]
# Create an image to draw on and an image to show the selection window
out_img = np.dstack((binary_warped, binary_warped, binary_warped))*255
window_img = np.zeros_like(out_img)
# Color in left and right line pixels
out_img[nonzeroy[left_lane_inds], nonzerox[left_lane_inds]] = [255, 0, 0]
out_img[nonzeroy[right_lane_inds], nonzerox[right_lane_inds]] = [0, 0, 255]
# Generate a polygon to illustrate the search window area
# And recast the x and y points into usable format for cv2.fillPoly()
left_line_window1 = np.array([np.transpose(np.vstack([left_fitx-margin, ploty]))])
left_line_window2 = np.array([np.flipud(np.transpose(np.vstack([left_fitx+margin,
ploty])))])
left_line_pts = np.hstack((left_line_window1, left_line_window2))
right_line_window1 = np.array([np.transpose(np.vstack([right_fitx-margin, ploty]))])
right_line_window2 = np.array([np.flipud(np.transpose(np.vstack([right_fitx+margin,
ploty])))])
right_line_pts = np.hstack((right_line_window1, right_line_window2))
# Draw the lane onto the warped blank image
cv2.fillPoly(window_img, np.int_([left_line_pts]), (0,255, 0))
cv2.fillPoly(window_img, np.int_([right_line_pts]), (0,255, 0))
result = cv2.addWeighted(out_img, 1, window_img, 0.3, 0)
plt.imshow(result)
plt.plot(left_fitx, ploty, color='yellow')
plt.plot(right_fitx, ploty, color='yellow')
plt.xlim(0, 1280)
plt.ylim(720, 0)
# Extract left and right line pixel positions
leftx = nonzerox[left_lane_inds]
lefty = nonzeroy[left_lane_inds]
rightx = nonzerox[right_lane_inds]
righty = nonzeroy[right_lane_inds]
return leftx, lefty, rightx, righty
leftx, lefty, rightx, righty = look_ahead_search(top_down, left_fit=left_fit, right_fit=right_fit, plot=True)
Determine the Curvature and Center Offset¶
In [33]:
def get_curvature(left_fit, right_fit, y_eval):
# Calculate the new radii of curvature
left_curverad = ((1 + (2*left_fit[0]*y_eval + left_fit[1])**2)**1.5) / np.absolute(2*left_fit[0]) if left_fit is not None else None
right_curverad = ((1 + (2*right_fit[0]*y_eval + right_fit[1])**2)**1.5) / np.absolute(2*right_fit[0]) if right_fit is not None else None
return left_curverad, right_curverad
left_fit, right_fit = fit_lines(leftx, lefty, rightx, righty)
left_curverad, right_curverad = get_curvature(left_fit, right_fit, top_down.shape[0])
print('curvature left: {} px, right: {} px'.format(left_curverad, right_curverad))
In [34]:
# Define conversions in x and y from pixels space to meters
ym_per_pix = 30/720 # meters per pixel in y dimension
xm_per_pix = 3.7/700 # meters per pixel in x dimension
def get_world_curvature(leftx, lefty, rightx, righty, y_eval):
if leftx is None or lefty is None or rightx is None or righty is None:
return None, None
# Fit new polynomials to x,y in world space
left_fit_cr = np.polyfit(lefty*ym_per_pix, leftx*xm_per_pix, 2)
right_fit_cr = np.polyfit(righty*ym_per_pix, rightx*xm_per_pix, 2)
# Calculate the new radii of curvature
left_curverad = ((1 + (2*left_fit_cr[0]*y_eval*ym_per_pix + left_fit_cr[1])**2)**1.5) / np.absolute(2*left_fit_cr[0])
right_curverad = ((1 + (2*right_fit_cr[0]*y_eval*ym_per_pix + right_fit_cr[1])**2)**1.5) / np.absolute(2*right_fit_cr[0])
return left_curverad, right_curverad
left_curverad, right_curverad = get_world_curvature(leftx, lefty, rightx, righty, top_down.shape[0])
print('curvature left: {} m, right: {} m'.format(left_curverad, right_curverad))
In [35]:
def get_base_poses(left_fit, right_fit, y_eval):
left_base_pose = left_fit[0]*y_eval**2 + left_fit[1]*y_eval + left_fit[2] if left_fit is not None else None
right_base_pose = right_fit[0]*y_eval**2 + right_fit[1]*y_eval + right_fit[2] if right_fit is not None else None
return left_base_pose, right_base_pose
def get_center_offset(left_base_pose, right_base_pose, image_width):
if not left_base_pose or not right_base_pose:
return None
lane_center = (left_base_pose + right_base_pose) / 2
center_offset = (lane_center - image_width/2)*xm_per_pix
return center_offset
left_base_pose, right_base_pose = get_base_poses(left_fit, right_fit, top_down.shape[0])
center_offset = get_center_offset(left_base_pose, right_base_pose, top_down.shape[1])
print('center offset {} m'.format(center_offset))
In [36]:
def draw_curvature(image, left_curverad, right_curverad):
new_image = np.copy(image)
curverad = (left_curverad + right_curverad)/2
cv2.putText(new_image, 'Radius of Curvature {:.0f}(m)'.format(curverad), (120,160),
fontFace = 16, fontScale = 2, color=(255,255,255), thickness = 3)
return new_image
curve_image = draw_curvature(test_img, left_curverad, right_curverad)
plt.imshow(curve_image)
Out[36]:
In [37]:
def draw_offset(image, center_offset):
new_image = np.copy(image)
side = 'left' if center_offset < 0 else 'right'
cv2.putText(new_image, 'Vehicle is {:.2f}m {} of center'.format(abs(center_offset), side), (100,80),
fontFace = 16, fontScale = 2, color=(255,255,255), thickness = 4)
return new_image
curve_offset_image = draw_offset(curve_image, center_offset)
plt.imshow(curve_offset_image)
Out[37]:
Inverse Transform¶
In [38]:
def map_lane(undist, warped, Minv, left_fit, right_fit):
# Create an image to draw the lines on
warp_zero = np.zeros_like(warped).astype(np.uint8)
color_warp = np.dstack((warp_zero, warp_zero, warp_zero))
if left_fit is not None and right_fit is not None:
ploty = np.linspace(0, warped.shape[0]-1, warped.shape[0] )
left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]
# Recast the x and y points into usable format for cv2.fillPoly()
pts_left = np.array([np.transpose(np.vstack([left_fitx, ploty]))])
pts_right = np.array([np.flipud(np.transpose(np.vstack([right_fitx, ploty])))])
pts = np.hstack((pts_left, pts_right))
# Draw the lane onto the warped blank image
cv2.fillPoly(color_warp, np.int_([pts]), (0,255, 0))
# Warp the blank back to original image space using inverse perspective matrix (Minv)
newwarp = cv2.warpPerspective(color_warp, Minv, (undist.shape[1], undist.shape[0]))
# Combine the result with the original image
result = cv2.addWeighted(undist, 1, newwarp, 0.3, 0)
return result
In [39]:
#test_image = mpimg.imread('test_images/test3.jpg')
#undist = cv2.undistort(test_image, mtx, dist, None, mtx)
result = map_lane(undist, top_down, Minv, left_fit, right_fit)
result = draw_curvature(result, left_curverad, right_curverad)
result = draw_offset(result, center_offset)
plt.imshow(result)
Out[39]:
Build an Advanced Lane Finding Pipeline¶
Build the pipeline and run the solution on all test images. Make copies into the test_images_output directory.
In [40]:
def pipeline(img):
#1. Undistort
undist = undistort(img)
#2. Gradient thresholded binary
thresholded = thresholded_binary(undist)
#3. Warp to top down
top_down, perspective_M, Minv = warper(thresholded, img.shape)
#4. Search and fit polynomial lines
leftx, lefty, rightx, righty, _ = sliding_window(top_down)
left_fit, right_fit = fit_lines(leftx, lefty, rightx, righty)
if left_fit is not None and right_fit is not None:
#5. Calculate curvature and center offset
left_curverad, right_curverad = get_world_curvature(leftx, lefty, rightx, righty, top_down.shape[0])
left_base_pose, right_base_pose = get_base_poses(left_fit, right_fit, top_down.shape[0])
center_offset = get_center_offset(left_base_pose, right_base_pose, top_down.shape[1])
#6. Draw the lane on image (and inverse transform)
new_image = map_lane(undist, top_down, Minv, left_fit, right_fit)
#7. Draw curvature and offset
new_image = draw_curvature(new_image, left_curverad, right_curverad)
new_image = draw_offset(new_image, center_offset)
else:
new_image = img
return new_image
In [41]:
test_fnames = glob.glob('test_images/test*.jpg')
n_col = 4
n_row = int(np.ceil(len(test_fnames)/n_col))
f, axs = plt.subplots(n_row, n_col, figsize=(20,3*n_row))
axs = axs.ravel()
for i in range(len(axs)):
if i < len(test_fnames):
axs[i].axis('off')
image = mpimg.imread(test_fnames[i])
processed = pipeline(image)
axs[i].imshow(processed)
axs[i].set_title(test_fnames[i])
else:
f.delaxes(axs[i])
Next, I'll run the pipeline on a video stream.
To do it, I had to keep track of things like where my last several detections of the lines were, and what the curvature was, so I could properly treat new detections.
I defined a Line() class to keep track of all the parameters I measure from frame to frame.
In [42]:
from collections import deque
class Line():
def __init__(self):
# was the line detected in the last iteration?
self.detected = False
# polynomial coefficients for the last n fits of the line
self.recent_fitted = deque(maxlen=3)
#polynomial coefficients averaged over the last n iterations
self.best_fit = None
#polynomial coefficients for the most recent fit
self.current_fit = [np.array([False])]
#radius of curvature of the line in some units
self.radius_of_curvature = None
#distance in meters of vehicle center from the line
self.line_base_pos = None
#difference in fit coefficients between last and new fits
self.diffs = np.array([0,0,0], dtype='float')
#x values for detected line pixels
self.allx = None
#y values for detected line pixels
self.ally = None
# number of failed detections
self.num_undetected = 100
def update_detected(self, line_fit, curvature, base_pose, linex, liney):
self.detected = True
self.diffs = line_fit - self.current_fit
self.current_fit = np.array(line_fit)
self.recent_fitted.append(line_fit)
self.best_fit = sum(self.recent_fitted) / len(self.recent_fitted)
self.radius_of_curvature = curvature
self.line_base_pos = base_pose
self.allx = linex
self.ally = liney
self.num_undetected = 0
def update_undetected(self):
self.detected = False
self.num_undetected += 1
left_line = Line()
right_line = Line()
In [43]:
# Sanity checks
def similar_curve(left_curve, right_curve):
diff = np.linalg.norm(left_curve - right_curve)
#print('curve diff {}, left {}, right {}'.format(diff, left_curve, right_curve))
return diff < 5000
def right_distance(left_fit, right_fit):
diff = np.linalg.norm(left_fit - right_fit)
#print('distance diff {}'.format(diff))
return diff > 100 and diff < 1200
def parallel(left_fit, right_fit):
left_slope = 2*left_fit[0]
right_slope = 2*right_fit[0]
diff = np.linalg.norm(left_slope - right_slope)
#print('slope diff {}, left {}, right {}'.format(diff, left_slope, right_slope))
return diff < 2e-3
def good_frame(left_fit, right_fit, left_curve, right_curve):
curve_good = similar_curve(left_curverad, right_curverad)
distance_good = right_distance(left_fit, right_fit)
slope_good = parallel(left_fit, right_fit)
#print('detection ' + str(curve_good) + ', ' + str(distance_good) + ', ' + str(slope_good))
return curve_good and distance_good and slope_good
In [44]:
undetected_count = 0
def video_pipeline(img):
def undetected(left_line, right_line, error_type):
global undetected_count
left_line.update_undetected()
right_line.update_undetected()
undetected_count += 1
mpimg.imsave('./output_images/undetected_{}_{}.jpg'.format(error_type, undetected_count), img)
#1. Undistort
undist = undistort(img)
#2. Gradient thresholded binary
thresholded = thresholded_binary(undist)
#3. Warp to top down
top_down, perspective_M, Minv = warper(thresholded, img.shape)
#4. Search and fit polynomial lines
if left_line.num_undetected > 3 or right_line.num_undetected > 3:
leftx, lefty, rightx, righty, _ = sliding_window(top_down)
left_fit, right_fit = fit_lines(leftx, lefty, rightx, righty)
else:
leftx, lefty, rightx, righty = look_ahead_search(top_down, left_fit=left_line.best_fit, right_fit=right_line.best_fit)
left_fit, right_fit = fit_lines(leftx, lefty, rightx, righty)
if left_fit is not None and right_fit is not None:
#5. Calculate curvature and center offset
left_curverad, right_curverad = get_world_curvature(leftx, lefty, rightx, righty, top_down.shape[0])
left_base_pose, right_base_pose = get_base_poses(left_fit, right_fit, top_down.shape[0])
# sanity check
if good_frame(left_fit, right_fit, left_curverad, right_curverad):
#print('good frame')
left_line.update_detected(left_fit, left_curverad, left_base_pose, leftx, lefty)
right_line.update_detected(right_fit, right_curverad, right_base_pose, rightx, righty)
else:
print('undetected1')
undetected(left_line, right_line,1)
else:
print('undetected2')
undetected(left_line, right_line,2)
new_image = img
if left_line.best_fit is not None and right_line.best_fit is not None:
center_offset = get_center_offset(left_line.line_base_pos, right_line.line_base_pos, top_down.shape[1])
#6. Draw the lane on image (and inverse transform)
new_image = map_lane(undist, top_down, Minv, left_line.best_fit, right_line.best_fit)
#7. Draw curvature and offset
new_image = draw_curvature(new_image, left_line.radius_of_curvature, right_line.radius_of_curvature)
new_image = draw_offset(new_image, center_offset)
return new_image
In [45]:
left_line = Line()
right_line = Line()
test_image = mpimg.imread('test_images/test7.jpg')
pipeline_result = video_pipeline(test_image)
plt.imshow(pipeline_result)
Out[45]:
Test on Videos¶
In [46]:
# Import everything needed to edit/save/watch video clips
from moviepy.editor import VideoFileClip
from IPython.display import HTML
In [47]:
def test_video(src_path, dst_path, subclip_range=None):
global left_line, right_line, undetected_count
left_line = Line()
right_line = Line()
undetected_count = 0
project_output = dst_path
if subclip_range is None:
clip1 = VideoFileClip(src_path)
else:
clip1 = VideoFileClip(src_path).subclip(subclip_range)
white_clip = clip1.fl_image(video_pipeline)
%time white_clip.write_videofile(project_output, audio=False)
In [48]:
test_video('project_video.mp4','test_videos_output/project_video.mp4')
In [49]:
test_video('challenge_video.mp4','test_videos_output/challenge_video.mp4')
In [50]:
test_video('harder_challenge_video.mp4','test_videos_output/harder_challenge_video.mp4')